Another trick
Brillhart = {{0, 2, 2}, {1, 0, 2}, {2, 1, 0}}; bc = Eigenvalues[Brillhart][[1]]; N[Log[(2 + bc)^24 - 24]/Sqrt[163], 34]
3.141592653589793238462643383279503
N[Pi, 34]
Ed, you might what to add this to the entry in the OEIS in the PROG section at least.
https://oeis.org/A002937
The 163 number is treated in
https://www.youtube.com/watch?v=DRxAVA6gYMM